Quarter the figs and process them in the food processor until the mixture is smooth.
Cake
Preheat the oven to 325° F/165° C. Set rack in the middle of the oven.
In the bowl of the stand mixer, cream the butter and sugar until it it light and fluffy.
Add the eggs, one at a time, beating well each time. Add the fig puree and vanilla extract, and mix until thoroughly combined.
In the medium bowl, sift together the flour, cinnamon, nutmeg, and baking soda. Add to the fig mixture and stir gently, tossing in the chopped figs. Do not over mix.
Pour the batter into the prepared pan. Bake for 60 to 75 minutes, checking every 5 minutes after 1 hour has passed. When a tester comes out dry with just a few crumbs clinging, remove the pan from the oven. If the tester has no crumbs the cake will be dry.
Cool the cake in the pan for 15 minutes, then turn the cake out onto a wire rack and cool completely.
Glaze
Warm the honey and butter in a small saucepan over low heat. Brush the warm glaze over the warm cake, and then again after the cake has cooled.
Allow the cake to rest overnight before serving. Store the cake in a cake keeper or on a cake stand with glass cover. The cake will stay moist for 2 to 3 days. Refrigerate or freeze any leftovers.